An Exact Black Hole Scattering Amplitude

TL;DR

This paper demonstrates that adding a NUT charge to black holes cancels orbital precession to all orders and proposes a generalized eikonal formula linking classical trajectories to quantum scattering amplitudes.

Contribution

It introduces a novel approach connecting classical integrability with quantum scattering amplitudes for black holes with NUT charge.

Findings

Precession vanishes to all orders with NUT charge.

Classical trajectories determine quantum amplitudes via exponentiation.

Discusses implications of integrability in self-dual gravity.

Abstract

General Relativity famously predicts precession of orbital motions in the Schwarzschild metric. In this paper we show that by adding a NUT charge $N = iM$ the precession vanishes to all orders in $G$ even for rotating black holes. Moreover, we conjecture a generalization of the eikonal formula and show that the classical integrable trajectories determine the full quantum amplitude for this black hole, by means of exponentiation of the Post-Minkowskian radial action. Several consequences of integrability in self-dual gravity are discussed.